Alternating Estimation Series Theorem

Hello,

I am having problems understanding Alternating Series Estimation Theorem...

http://i39.tinypic.com/k9uwc9.png

For the 2nd half of the question (finding the natural number of n)... (ignore the equal signs, I was getting desperate), I thought that like the other tests like convergence, limit comparison, etc that

with the error being the 0.004?

But that is apparently wrong. I double checked my algebra and it is correct... so it is just a signage error.

If anybody could even give a hint, that would be greatly appreciated... this whole chapter on series and sequences is confusing.

Thanks a bunch?